Math & Kinematics

Euler Angles

Euler Angles are a parameterization of 3D orientation as three successive rotations about specified axes, with conventions such as ZYX yaw-pitch-roll common in robotics and aerospace. They are minimal and human-readable but suffer from gimbal lock, a singularity where two rotation axes align and a degree of freedom is lost, and from convention ambiguity across tools. Quaternions and rotation matrices are preferred for computation, with Euler angles retained for interfaces and displays.

Why it matters for physical AI

Orientation representation choices propagate into learned systems: regressing Euler angles introduces discontinuities and singularities that degrade pose estimation and policy outputs, motivating quaternion or 6D rotation parameterizations.